6. Consider the rings 2Z = {2k: k E Z} and 8Z = {8m: m =...

 

Transcribed Image Text:

6. Consider the rings 2Z = {2k: k E Z} and 8Z = {8m: m = Z}. a. Verify that 8Z is an ideal of 2Z b. Describe the elements of 2Z/8Z c. Construct addition and multiplication tables for 2Z/8Z d. Determine whether 2Z/8Z is isomorphic to Z4. 7. Find all constants c E Z5 such that Z5[x]/(x + x + c) is a field. 6. Consider the rings 2Z = {2k: k E Z} and 8Z = {8m: m = Z}. a. Verify that 8Z is an ideal of 2Z b. Describe the elements of 2Z/8Z c. Construct addition and multiplication tables for 2Z/8Z d. Determine whether 2Z/8Z is isomorphic to Z4. 7. Find all constants c E Z5 such that Z5[x]/(x + x + c) is a field.